Subgroups — #30649205

Order 16256.

564 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16861241	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16861236	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16861232	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×SD₁₆×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#22550451	C₂	1	1	yes	maximal, characteristic, complemented
6	#22550444	C₂	1	1	yes	maximal, characteristic, complemented
7	#22550269	C₂	1	1	yes	maximal, characteristic, complemented
8	#22550265	C₂	1	1	yes	maximal, characteristic, complemented
9	#22550262	C₂	1	1	yes	maximal, characteristic, complemented
10	#22550261	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550258	C₂	1	1	yes	maximal, characteristic, complemented
12	#22550250	C₂	1	1	yes	maximal, characteristic, complemented
13	#22550247	C₂	1	1	yes	maximal, characteristic, complemented
14	#22549833	C₂	1	1	yes	maximal, characteristic, complemented
15	#497×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14523249	C₂²	1	1	yes	characteristic
17	C₂×#14523249	C₂²	1	1	yes	characteristic
18	C₂×Q₈×D₁₂₇	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic
20	#16861241	—	2	4	no	—
21	#16861236	—	2	4	no	—
22	#16861232	—	2	4	no	—
23	C₂×#14523238	C₂²	1	1	yes	characteristic, complemented
24	C₂×#14523237	C₂²	1	1	yes	characteristic
25	C₂×#14523237	C₂²	1	1	yes	characteristic, complemented
26	C₂×#14523236	C₂²	1	1	yes	characteristic
27	C₂×#14523235	C₂²	1	1	yes	characteristic
28	C₂×#14523235	C₂²	1	1	yes	characteristic
29	C₂×#14523235	C₂²	1	1	yes	characteristic, complemented
30	C₂×#14523235	C₂²	1	1	yes	characteristic, complemented
31	C₂×#14523235	C₂²	1	1	yes	characteristic, complemented
32	SD₁₆×D₁₂₇	—	2	4	no	—
33	C₂×D₁₀₁₆	C₂²	1	1	yes	characteristic
34	C₂×D₁₀₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₂×#14523233	C₂²	1	1	yes	characteristic
36	C₂×#14523231	C₂²	1	1	yes	characteristic
37	C₂×C₈×D₁₂₇	C₂²	1	1	yes	characteristic
38	#16861207	C₂²	1	1	yes	characteristic, complemented
39	#16861206	C₂²	1	1	yes	characteristic
40	#16861205	C₂²	1	1	yes	characteristic
41	#16861198	C₂²	1	1	yes	characteristic
42	#16861198	C₂²	1	1	yes	characteristic, complemented
43	#16861197	C₂²	1	1	yes	characteristic, complemented
44	#16861194	—	2	2	no	—
45	#16861187	—	2	2	no	—
46	#16861182	—	2	2	no	—
47	#16861179	—	2	2	no	—
48	#16861166	C₂²	1	1	yes	characteristic
49	#16861119	C₂²	1	1	yes	characteristic, complemented
50	C₄×C₁₂₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	C₈×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
52	C₂×Q₁₆×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
53	C₂×Q₁₆×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
54	C₂×SD₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
55	C₂×SD₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
56	C₄⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
57	#124×C₁₂₇	C₂²	1	1	yes	characteristic
58	#97×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₁₂₇	—	2	1	no	—
60	#14523249	—	2	2	no	—
61	#14523249	—	2	2	no	—
62	#14523249	—	2	2	no	—
63	#14523249	—	2	2	no	—
64	C₂×Dic₂₅₄	—	2	1	no	—
65	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
66	Q₈×D₁₂₇	—	2	2	no	—
67	Q₈×D₁₂₇	—	2	2	no	—
68	C₂×D₅₀₈	—	2	1	no	—
69	C₂×D₅₀₈	—	2	1	no	—
70	C₂×D₅₀₈	—	2	2	no	—
71	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
72	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
73	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊D₁₂₇	—	2	1	no	—
75	C₂×C₂²⋊D₁₂₇	—	2	2	no	—
76	D₄×D₁₂₇	—	2	2	no	—
77	D₄×D₁₂₇	—	2	2	no	—
78	C₂×C₄×D₁₂₇	—	2	1	no	—
79	C₂×C₄×D₁₂₇	—	2	1	no	—
80	C₂×C₄×D₁₂₇	—	2	1	no	—
81	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
82	#14523238	—	2	2	no	—
83	#14523237	—	2	2	no	—
84	#14523237	—	2	2	no	—
85	#14523236	—	2	2	no	—
86	#14523235	—	2	2	no	—
87	#14523235	—	2	2	no	—
88	#14523235	—	2	2	no	—
89	#14523235	—	2	2	no	—
90	#14523235	—	2	2	no	—
91	D₁₀₁₆	—	2	2	no	—
92	D₁₀₁₆	—	2	2	no	—
93	#14523233	—	2	2	no	—
94	#14523231	D₄	1	4	yes	complemented
95	C₂×C₁₂₇⋊C₈	C₂³	1	1	yes	characteristic
96	C₂×C₁₂₇⋊C₈	C₂³	1	1	yes	characteristic
97	C₈×D₁₂₇	D₄	1	4	yes	complemented
98	Dic₁₂₇⋊C₄	—	2	2	no	—
99	Dic₁₂₇⋊C₄	D₄	1	2	yes	—
100	(C₂×D₁₂₇)⋊C₄	—	2	2	no	—
101	(C₂×D₁₂₇)⋊C₄	—	2	2	no	—
102	(C₂×D₁₂₇)⋊C₄	—	2	2	no	—
103	(C₂×D₁₂₇)⋊C₄	D₄	1	2	yes	—
104	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
105	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
106	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
107	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
109	Q₁₆×C₁₂₇	—	2	2	no	—
110	Q₁₆×C₁₂₇	—	2	2	no	—
111	SD₁₆×C₁₂₇	—	2	2	no	—
112	SD₁₆×C₁₂₇	—	2	2	no	—
113	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
114	C₂×C₈×C₁₂₇	C₂³	1	1	yes	characteristic
115	C₄⋊C₄×C₁₂₇	—	2	2	no	—
116	C₂²⋊C₄×C₁₂₇	—	2	2	no	—
117	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
118	C₂²×D₁₂₇	—	2	1	no	—
119	C₂²×D₁₂₇	—	2	1	no	—
120	C₂²×D₁₂₇	—	2	1	no	—
121	C₂²×D₁₂₇	—	4	2	no	—
122	C₂²×D₁₂₇	—	8	2	no	—
123	C₂²×D₁₂₇	C₂×D₄	1	1	yes	characteristic
124	Dic₂₅₄	—	2	1	no	—
125	Dic₂₅₄	—	2	1	no	—
126	Dic₂₅₄	—	4	2	no	—
127	D₅₀₈	—	2	1	no	—
128	D₅₀₈	—	2	1	no	—
129	D₅₀₈	—	2	1	no	—
130	D₅₀₈	—	2	1	no	—
131	D₅₀₈	—	2	1	no	—
132	D₅₀₈	—	2	1	no	—
133	D₅₀₈	—	4	2	no	—
134	D₅₀₈	—	4	2	no	—
135	D₅₀₈	—	8	2	no	—
136	C₂²⋊D₁₂₇	—	4	2	no	—
137	C₂²⋊D₁₂₇	—	8	2	no	—
138	C₂×Dic₁₂₇	—	2	1	no	—
139	C₂×Dic₁₂₇	C₂×D₄	1	2	yes	—
140	C₂×Dic₁₂₇	C₂×D₄	1	1	yes	characteristic
141	C₄×D₁₂₇	—	4	2	no	—
142	C₄×D₁₂₇	—	4	2	no	—
143	C₄×D₁₂₇	—	4	2	no	—
144	C₄×D₁₂₇	C₂×D₄	1	2	yes	—
145	C₄×D₁₂₇	C₂×D₄	1	2	yes	—
146	C₁₂₇⋊C₈	C₂×D₄	1	2	yes	—
147	C₁₂₇⋊C₈	C₂×D₄	1	2	yes	—
148	C₂³×C₁₂₇	—	2	1	no	—
149	Q₈×C₁₂₇	—	2	1	no	—
150	Q₈×C₁₂₇	—	2	1	no	—
151	Q₈×C₁₂₇	—	2	1	no	—
152	Q₈×C₁₂₇	—	2	1	no	—
153	Q₈×C₁₂₇	—	2	1	no	—
154	Q₈×C₁₂₇	—	2	1	no	—
155	D₄×C₁₂₇	—	2	1	no	—
156	D₄×C₁₂₇	—	2	1	no	—
157	C₂×C₄×C₁₂₇	—	2	1	no	—
158	C₂×C₄×C₁₂₇	—	2	1	no	—
159	C₂×C₄×C₁₂₇	—	2	1	no	—
160	C₂×C₄×C₁₂₇	C₂×D₄	1	2	yes	—
161	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
162	C₈×C₁₂₇	C₂×D₄	1	2	yes	—
163	C₈×C₁₂₇	C₂×D₄	1	2	yes	—
164	C₂²×C₁₂₇	—	4	1	no	—
165	C₂²×C₁₂₇	—	4	2	no	—
166	C₂²×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×D₁₂₇	—	2	2	no	—
168	C₂×D₁₂₇	—	4	1	no	—
169	C₂×D₁₂₇	—	4	1	no	—
170	C₂×D₁₂₇	—	4	1	no	—
171	C₂×D₁₂₇	—	4	2	no	—
172	C₂×D₁₂₇	—	4	2	no	—
173	C₂×D₁₂₇	—	4	2	no	—
174	C₂×D₁₂₇	—	8	4	no	—
175	C₂×D₁₂₇	#127	1	2	yes	—
176	C₄×C₁₂₇	—	2	2	no	—
177	C₄×C₁₂₇	—	4	1	no	—
178	C₄×C₁₂₇	—	4	1	no	—
179	C₄×C₁₂₇	—	4	1	no	—
180	C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
181	C₄×C₁₂₇	C₂²×D₄	1	1	yes	characteristic
182	Dic₁₂₇	—	2	2	no	—
183	Dic₁₂₇	—	4	1	no	—
184	Dic₁₂₇	#127	1	2	yes	—
185	C₂×C₁₂₇	—	8	1	no	—
186	C₂×C₁₂₇	C₂×#127	1	1	yes	characteristic
187	C₂×C₁₂₇	#577	1	2	yes	—
188	D₁₂₇	—	2	2	no	—
189	D₁₂₇	—	8	1	no	—
190	D₁₂₇	—	8	1	no	—
191	D₁₂₇	—	8	1	no	—
192	#3154	—	127	1	no	maximal, Sylow
193	C₁₂₇	#3154	1	1	yes	characteristic, complemented, Sylow
194	C₂×#137	—	127	1	no	—
195	C₂×AGL(1,ℤ/8)	—	127	1	no	—
196	C₂×#135	—	127	1	no	—
197	C₂²×SD₁₆	—	127	1	no	—
198	#536	—	127	1	no	—
199	#535	—	127	1	no	—
200	#497	—	127	1	no	—
201	#497	D₁₂₇	1	1	yes	characteristic, complemented
202	#496	—	127	1	no	—
203	#496	—	127	1	no	—
204	#495	—	127	1	no	—
205	#495	—	127	1	no	—
206	#492	—	127	1	no	—
207	#492	—	127	1	no	—
208	#405	—	127	1	no	—
209	C₂×#41	—	127	1	no	—
210	C₂×#41	—	127	1	no	—
211	C₂²×Q₈	—	127	1	no	—
212	C₂²×D₄	—	127	1	no	—
213	#137	—	254	4	no	—
214	AGL(1,ℤ/8)	—	254	4	no	—
215	#135	—	254	4	no	—
216	C₂×Q₁₆	—	127	1	no	—
217	C₂×Q₁₆	C₂×D₁₂₇	1	1	yes	characteristic, complemented
218	C₂×Q₁₆	C₂×D₁₂₇	1	1	yes	characteristic, complemented
219	C₂×SD₁₆	—	127	1	no	—
220	C₂×SD₁₆	—	127	1	no	—
221	C₂×SD₁₆	—	127	1	no	—
222	C₂×SD₁₆	—	127	1	no	—
223	C₂×SD₁₆	—	127	1	no	—
224	C₂×SD₁₆	—	127	1	no	—
225	C₂×SD₁₆	—	127	1	no	—
226	C₂×SD₁₆	—	127	1	no	—
227	C₂×SD₁₆	—	254	4	no	—
228	C₂×SD₁₆	C₂×D₁₂₇	1	1	yes	characteristic
229	C₂×SD₁₆	C₂×D₁₂₇	1	1	yes	characteristic
230	C₂×D₈	—	127	1	no	—
231	C₂×D₈	—	127	1	no	—
232	C₂×D₈	—	127	1	no	—
233	C₂×M₁₆	—	127	1	no	—
234	C₂²×C₈	—	127	1	no	—
235	C₄⋊Q₈	—	127	1	no	—
236	C₄⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
237	#127	—	127	1	no	—
238	#127	—	127	1	no	—
239	#124	—	127	1	no	—
240	#124	—	127	1	no	—
241	#124	—	127	1	no	—
242	#124	C₂×D₁₂₇	1	1	yes	characteristic
243	#123	—	254	2	no	—
244	C₂²⋊Q₈	—	254	2	no	—
245	#121	—	254	2	no	—
246	#120	—	254	2	no	—
247	#117	—	127	1	no	—
248	#97	—	127	1	no	—
249	#97	C₂×D₁₂₇	1	1	yes	characteristic, complemented
250	C₄×C₈	—	127	1	no	—
251	C₄×C₈	—	127	1	no	—
252	C₂⁴	—	254	1	no	—
253	#41	—	254	2	no	—
254	#41	—	254	2	no	—
255	#41	—	254	2	no	—
256	#41	—	254	2	no	—
257	C₂×Q₈	—	127	1	no	—
258	C₂×Q₈	—	254	1	no	—
259	C₂×Q₈	—	254	2	no	—
260	C₂×Q₈	—	254	2	no	—
261	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
262	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
263	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
264	C₂×D₄	—	127	1	no	—
265	C₂×D₄	—	127	1	no	—
266	C₂×D₄	—	127	1	no	—
267	C₂×D₄	—	254	1	no	—
268	C₂×D₄	—	254	1	no	—
269	C₂×D₄	—	254	2	no	—
270	C₂×D₄	—	254	2	no	—
271	C₂×D₄	—	254	2	no	—
272	C₂×D₄	—	254	1	no	—
273	C₂×D₄	—	254	2	no	—
274	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
275	C₂²×C₄	—	127	1	no	—
276	C₂²×C₄	—	254	1	no	—
277	C₂²×C₄	—	254	1	no	—
278	C₂²×C₄	—	254	1	no	—
279	Q₁₆	—	2	2	no	—
280	Q₁₆	—	2	2	no	—
281	Q₁₆	—	254	2	no	—
282	SD₁₆	—	2	2	no	—
283	SD₁₆	—	2	2	no	—
284	SD₁₆	—	254	2	no	—
285	SD₁₆	—	254	2	no	—
286	SD₁₆	—	254	2	no	—
287	SD₁₆	—	254	2	no	—
288	SD₁₆	—	254	2	no	—
289	SD₁₆	—	254	2	no	—
290	SD₁₆	—	254	2	no	—
291	SD₁₆	—	254	2	no	—
292	D₈	—	254	2	no	—
293	D₈	—	254	2	no	—
294	D₈	—	254	2	no	—
295	M₁₆	—	127	4	no	—
296	C₂×C₈	—	127	1	no	—
297	C₂×C₈	—	127	1	no	—
298	C₂×C₈	—	127	4	no	—
299	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
300	C₂×C₈	C₂²×D₁₂₇	1	1	yes	characteristic
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	127	2	no	—
303	C₄⋊C₄	—	254	2	no	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	127	2	no	—
306	C₂²⋊C₄	—	254	2	no	—
307	C₂²⋊C₄	—	254	2	no	—
308	C₂²⋊C₄	—	254	2	no	—
309	C₄²	—	127	1	no	—
310	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
311	C₂³	—	2	1	no	—
312	C₂³	—	127	1	no	—
313	C₂³	—	1016	2	no	—
314	C₂³	—	508	2	no	—
315	C₂³	—	254	1	no	—
316	C₂³	—	254	1	no	—
317	C₂³	—	254	1	no	—
318	Q₈	—	2	1	no	—
319	Q₈	—	2	1	no	—
320	Q₈	—	2	1	no	—
321	Q₈	—	2	1	no	—
322	Q₈	—	2	1	no	—
323	Q₈	—	2	1	no	—
324	Q₈	—	508	2	no	—
325	Q₈	—	254	1	no	—
326	Q₈	—	254	1	no	—
327	D₄	—	2	1	no	—
328	D₄	—	2	1	no	—
329	D₄	—	1016	2	no	—
330	D₄	—	1016	2	no	—
331	D₄	—	508	2	no	—
332	D₄	—	508	2	no	—
333	D₄	—	508	2	no	—
334	D₄	—	254	1	no	—
335	D₄	—	254	1	no	—
336	D₄	—	254	1	no	—
337	D₄	—	254	1	no	—
338	D₄	—	254	1	no	—
339	D₄	—	254	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	127	1	no	—
344	C₂×C₄	—	127	2	no	—
345	C₂×C₄	—	127	2	no	—
346	C₂×C₄	—	127	2	no	—
347	C₂×C₄	—	508	2	no	—
348	C₂×C₄	—	508	2	no	—
349	C₂×C₄	—	508	2	no	—
350	C₂×C₄	—	254	1	no	—
351	C₂×C₄	D₄×D₁₂₇	1	2	yes	—
352	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
353	C₈	—	127	2	no	—
354	C₈	—	127	2	no	—
355	C₈	D₄×D₁₂₇	1	2	yes	—
356	C₈	D₄×D₁₂₇	1	2	yes	—
357	C₂²	—	4	1	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	127	2	no	—
360	C₂²	—	1016	4	no	—
361	C₂²	—	508	1	no	—
362	C₂²	—	508	1	no	—
363	C₂²	—	508	1	no	—
364	C₂²	—	508	2	no	—
365	C₂²	—	508	2	no	—
366	C₂²	—	508	2	no	—
367	C₂²	—	254	2	no	—
368	C₂²	C₂×D₄×D₁₂₇	1	1	yes	characteristic
369	C₄	—	2	2	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	1	no	—
373	C₄	—	127	2	no	—
374	C₄	—	508	1	no	—
375	C₄	—	254	2	no	—
376	C₄	C₂×D₄×D₁₂₇	1	1	yes	characteristic
377	C₄	C₂×D₄×D₁₂₇	1	1	yes	characteristic
378	C₂	—	8	1	no	—
379	C₂	—	1016	1	no	—
380	C₂	—	1016	1	no	—
381	C₂	—	1016	1	no	—
382	C₂	—	254	2	no	—
383	C₂	#127×D₁₂₇	1	1	yes	characteristic
384	C₂	#22550685	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₂₇
commutator, cosocle	C₂×C₄×C₁₂₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₂₇
Fitting	#497×C₁₂₇	C₂
socle	C₂²×C₁₂₇	C₂²×D₄
hypercenter	#497	D₁₂₇
hypocenter	C₁₂₇	#3154
LCS	G ▷ C₂×C₄×C₁₂₇ ▷ C₂×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #497

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#16861241	C₂	semidirect
2. C₂×#16861236	C₂	semidirect
3. C₂×#16861232	C₂	semidirect
4. C₂×SD₁₆×D₁₂₇	C₂	semidirect
5. #22550451	C₂	semidirect
6. #22550444	C₂	semidirect
7. #22550269	C₂	semidirect
8. #22550265	C₂	semidirect
9. #22550262	C₂	semidirect
10. #22550261	C₂	semidirect
11. #22550258	C₂	semidirect
12. #22550250	C₂	semidirect
13. #22550247	C₂	semidirect
14. #22549833	C₂	semidirect
15. #497×C₁₂₇	C₂	semidirect
23. C₂×#14523238	C₂²	semidirect
25. C₂×#14523237	C₂²	semidirect
29. C₂×#14523235	C₂²	semidirect
30. C₂×#14523235	C₂²	semidirect
31. C₂×#14523235	C₂²	semidirect
34. C₂×D₁₀₁₆	C₂²	semidirect
38. #16861207	C₂²	semidirect
42. #16861198	C₂²	semidirect
43. #16861197	C₂²	semidirect
49. #16861119	C₂²	semidirect
50. C₄×C₁₂₇⋊C₈	C₂²	semidirect
51. C₈×Dic₁₂₇	C₂²	semidirect
52. C₂×Q₁₆×C₁₂₇	C₂²	semidirect
53. C₂×Q₁₆×C₁₂₇	C₂²	semidirect
56. C₄⋊Q₈×C₁₂₇	C₂²	semidirect
58. #97×C₁₂₇	C₂²	semidirect
94. #14523231	D₄	semidirect
97. C₈×D₁₂₇	D₄	semidirect
193. C₁₂₇	#3154	semidirect
201. #497	D₁₂₇	semidirect
217. C₂×Q₁₆	C₂×D₁₂₇	semidirect
218. C₂×Q₁₆	C₂×D₁₂₇	semidirect
236. C₄⋊Q₈	C₂×D₁₂₇	semidirect
249. #97	C₂×D₁₂₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#16861241	2
C₂×#16861236	2
C₂×#16861232	2
C₂×SD₁₆×D₁₂₇	2
#22550451	2
#22550444	2
#22550269	2
#22550265	2
#22550262	2
#22550261	2
#22550258	2
#22550250	2
#22550247	2
#22549833	2
#497×C₁₂₇	2
#3154	127